7. A force $$ F_{1} $$ of 5 N and a force $$ \mathrm{F}_{2} $$ of 3 N are simultaneously exerted on an object. The direction of the forces can be altered at will. 7.1 When will these forces have their greatest resultant? 7.2 Confirm your answer in 7.1 by determining the resultant of these forces, utilizing an accurate tail--o-head vector diagram. Use a scale of $$ 10 \mathrm{~mm}: 1 \mathrm{~N} $$. 7.3 Test your answer in Question 7.2 by using a vector equation. 7.4 When will these forces have their least resultant? 7.5 Confirm your answers in Question 7.4 by determining the resultant of these forces, utilzing an accurate tal- to-head vector diagram. Use a scale of 10 mm : 1 N

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UpStudy AI · Accepted Answer

To find when the forces will have their greatest resultant, we need to consider the direction of the forces. The resultant of two forces is maximum when the forces are in the same direction.

Given:
- Force $$ F_{1} = 5 \, 	ext{N} $$
- Force $$ F_{2} = 3 \, 	ext{N} $$

The greatest resultant will occur when both forces are in the same direction. This means that the forces should be aligned in the same direction to maximize the resultant.

To confirm this, we can use a vector diagram with a scale of $$ 10 \, 	ext{mm} : 1 \, 	ext{N} $$ to visualize the forces and their resultant.

For the least resultant, the forces should be in opposite directions. This means that the forces should be aligned in opposite directions to minimize the resultant.

Let's calculate the resultant of the forces using a vector equation to confirm our answers.
Calculate the value by following steps:
- step0: Calculate:
  $$5+3$$
- step1: Add the numbers:
  $$8$$
The resultant of the forces $$ F_{1} = 5 \, 	ext{N} $$ and $$ F_{2} = 3 \, 	ext{N} $$ is $$ 8 \, 	ext{N} $$.

Therefore, the forces will have their greatest resultant when they are in the same direction, and the least resultant when they are in opposite directions.
When the forces are in the same direction, their resultant is greatest (8 N). When they are in opposite directions, the resultant is least (2 N).

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